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Svetlana Yu. Bogacheva
Kosygin Russian State University (Technologies. Design. Art)
Aleksandr V. Meshcheryakov
Kosygin Russian State University (Technologies. Design. Art)
Tatiana L. Gol'ceva
Kosygin Russian State University (Technologies. Design. Art)
ANALYTICAL MODELLING OF THREAD TENSION ON A SYSTEM OF SURFACES
Bogacheva S. Yu., Meshcheryakov A. V., Gol'ceva T. L. Analytical modelling of thread tension on a system of surfaces. Technologies & Quality. 2022. Nr 3(57). P. 14–19. (In Russ.) https://doi.org//10.34216/2587-6147-2022-3-57-14-19.
DOI: https://doi.org/10.34216/2587-6147-2022-3-57-14-19
УДК: 677.017.4:531
EDN: UACNLF
Publish date: 2022-10-07
Annotation: The paper deals with the determination of the tension of a flexible thread using numerical methods. The equilibrium of a homogeneous inextensible heavy thread, when statically interacting with a system of surfaces of various shapes, has been simulated. The paper presents the results of analytical modelling of thread tension. The formulas for calculating the tension at any point of thread by characteristic sections and the normal pressure at critical points have been derived. An example of calculation of thread tension on two smooth cylindrical surfaces and a rough surface of a cone simulating some working bodies of textile machines has been given. The normal pressure on the thread sections at the points dangerous, with respect to contact disturbance, has been determined. After solving all the equations and determining their components, a mathematical model of heavy thread tension at static equilibrium has been constructed using the points found.
Keywords: flexible homogeneous thread, equilibrium, tension, equilibrium equation, small slack arrow, equilibrium on smooth surface, equilibrium on rough surface
Literature list: 1. Bogacheva S. Yu. Thread tension detection method on the surfaces of working bodies // Fundamental and applied scientific research in the field of inclusive design and technology: experience, practice and prospects: a collection of scientific papers of the International Scientific and Practical Conference, March 24–26, 2021, Kosygin Russian State University (Technologies. Design. Art). Moscow, Kosygin Russian St. Univ. Publ., 2021. Р. 29–33. (In Russ.) 2. Bogacheva S. Yu. Analytical modeling of thread tension on cylindrical surfaces // Modern engineering problems of key industries. Modern problems of engineering sciences: a collection of scientific papers of the International Scientific and Technical Symposium and the III International Kosygin Forum, October 20–21, 2021, Kosygin Russian State University (Technologies. Design. Art). Moscow, Kosygin Russian St. Univ. Publ., 2021. Р. 67–70. (In Russ.) 3. Bogacheva S. Yu. Method for determining thread tension. Avtomatizirovannoe proektirovanie v mashinostroenii [Automated design in mechanical engineering]. 2020;9:44–47. (In Russ.) 4. Merkin D. R. Introduction to the mechanics of flexible thread. Moscow, Nauka Publ., 1980. 240 p. (In Russ.) 5. Bogacheva S. Yu., Belousova E. G. Determining the conditions of equilibrium and tension of an ideal thread on a conical surface // 54th International Scientific and Technical Conference of Teachers and Students: materials of the conference reports, April 28, 2021.Vitebsk, Vitebskij State tekhnologicheskij University Publ., 2021;1:210–213. (In Russ.) 6. Klochkova G. M. Application of the theory of a flexible thread to solving engineering problems: guidelines. Moscow, Kosygin Russian State University, 1993. 75 p. (In Russ.)
Author's info: Svetlana Yu. Bogacheva, Kosygin Russian State University (Technologies. Design. Art), Moscow, Russia, bogacheva-su@rguk.ru, https://orcid.org/0000-0002-2854-3213
Co-author's info: Aleksandr V. Meshcheryakov, Kosygin Russian State University (Technologies. Design. Art), Moscow, Russia, meshheryakov-av@rguk.ru, https://orcid.org/0000-0003-1655-4027
Co-author's info: Tatiana L. Gol'ceva, Kosygin Russian State University (Technologies. Design. Art), Moscow, Russia, goltseva-tl@rguk.ru, https://orcid.org/0000-0002-8622-7999